2015/11/10 by Thierry Bodineau, Isabelle Gallagher, Bodineau, Thierry +3 · 3 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Phase Equilibria and Thermodynamics
paper · doi:10.48550/arxiv.1511.03057
openalex publication_date 2015/11/10 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/30
We derive the linear acoustic and Stokes-Fourier equations as the limiting dynamics of a system of N hard spheres of diameter ε in two space dimensions, when N → ∞, ε → 0, N ε = α → ∞, using the linearized Boltzmann equation as an intermediate step. Our proof is based on Lanford's strategy [18], and on the pruning procedure developed in [5] to improve the convergence time to all kinetic times with a quantitative control which allows us to reach also hydrodynamic time scales. The main novelty here is that uniform L 2 a pri-ori estimates combined with a subtle symmetry argument provide a weak version of chaos, in the form of a cumulant expansion describing the asymptotic decorrelation between the particles. A refined geometric analysis of recollisions is also required in order to discard the possibility of multiple recollisions.